The present invention relates to a directional coupler switch in a dispersion relationship of a region of part of a parallel waveguide is changed due to a nonlinear action to change an exit of light entering from an input side, thereby functioning as an optical switch.
FIG. 1 shows a section view of a symmetric parallel waveguide, and a conceptual diagram of an even mode and an odd mode which are eigen modes thereof. Two waveguides of the symmetric parallel waveguide are referred to as A and B, respectively, and each of the waveguides has an even mode and an odd mode as its eigen modes.
FIG. 2A is a diagram showing superposition of the even mode on the odd mode, and FIG. 2B is a diagram showing superposition of the even mode on the odd mode in which the phase is inverted with respect to FIG. 2A. As shown in the figure, by inverting the phase, it is possible to laterally interchange electromagnetic distribution positions after superposition. When the even mode and the odd mode are added in a specific phase, light is concentrated on one of the waveguides (for example, the waveguide A) (FIG. 2A). When the even mode and the odd mode are added after inverting the phase (shifting by π), it is possible to represent a condition where light is concentrated on the waveguide B, conversely (FIG. 2B).
FIG. 3A is a diagram showing an initial condition in which output is performed from a waveguide that is opposite to the input waveguide, and FIG. 3B is a diagram showing a condition where the output waveguide is switched over by enhancing the intensity of coupling, so that output is performed from the waveguide which is the same as the input waveguide. When a phase difference between the even mode and the odd mode on the output side can be changed by π by means of external control, the output can be intentionally switched over between A and B, thereby causing the parallel waveguide to function as a switch.
(Description of a Structure in which a Refractive Index Variable Section, and a Refractive Index Fixed Section are Separately Provided)
FIG. 4 is a schematic diagram of a directional coupler switch. A region 1 is a portion which is subjected to a nonlinear action, and a region 2 is a portion which is not subjected to the action. The dispersion relationship in the region 1 is varied due to the nonlinear action, so that the exit of light entering from the input side is changed from an off-state output to an on-state output, thereby causing the switch to function as an optical switch.
Switching is performed by the variation of a dispersion curve due to the nonlinear effect.
The length of a portion in which the variation is performed (the region 1) is Lsw, and the length of a portion in which the variation is not performed (the region 2) is Lfix.
The switch-off state is defined as a condition in which light is emitted from a waveguide on an opposite side to the incident waveguide, after the light is propagated through the regions 1 and 2.
The switch-on state is defined as a condition in which light is emitted from a waveguide on the same side as the incident waveguide, after the light is propagated through the regions 1 and 2.
The wave numbers of the even mode and the odd mode of the region 2 are represented by k2e and k2o.
The wave numbers of the region 1 in the switch-off state are represented by k1e,off and k1o,off.
The wave numbers of the region 1 in the switch-on state are represented by k1e,on and k1o,on.
The switch-off state satisfies the following expression:
[Ex 1]Lsw(k2e,off−k2o,off)+Lfix(k2e−k2o)=(2m+1)π: m is an arbitrary integer  (1)
The switch-on state satisfies the following expression:
[Ex 2]Lsw(k1e,on−k1o,on)+Lfix(k2e−k2o)=2lπis an arbitrary integer  (2)
When a structure which satisfies the conditions is produced, it is possible to realize a directional coupler switch.
(Description of Switching Length)
When a difference between Expressions (2) and (1) is obtained, the following is held:
[Ex. 3]Lsw{(k1e,on−k1o,on)−(k1e,off−k1o,off)}=(2m+1)π: m is an arbitrary integer  (3)Lse is referred to as a switching length.(Conditions for Shortening the Switching Length)
The switching length is represented by the following:
[Ex. 4]
                                                                        L                sw                            =                            ⁢                                                                    (                                                                  2                        ⁢                        m                                            +                      1                                        )                                    ⁢                  π                                                                      (                                                                  k                                                                              1                            ⁢                            e                                                    ,                          on                                                                    -                                              k                                                                              1                            ⁢                            o                                                    ,                          on                                                                                      )                                    -                                      (                                                                  k                                                                              1                            ⁢                            e                                                    ,                          off                                                                    -                                              k                                                                              1                            ⁢                            o                                                    ,                          off                                                                                      )                                                                                                                          =                            ⁢                                                                    (                                                                  2                        ⁢                        m                                            +                      1                                        )                                    ⁢                  π                                                                      (                                                                  k                                                                              1                            ⁢                            e                                                    ,                          on                                                                    -                                              k                                                                              1                            ⁢                            e                                                    ,                          off                                                                                      )                                    -                                      (                                                                  k                                                                              1                            ⁢                            o                                                    ,                          on                                                                    -                                              k                                                                              1                            ⁢                            o                                                    ,                          off                                                                                      )                                                                                                          (        4        )            The dispersion relationships in the even and odd modes are represented by ω1e (k,n) and ω1o (k,n). In the expression, n is a parameter which indicates a factor for varying the dispersion curve such as a refractive index of a medium. As for the even mode, a total differential is obtained as follows:
[Ex. 5]
                              ⅆ                      ω                          1              ⁢              e                                      =                                                            ∂                                  ω                                      1                    ⁢                    e                                                                              ∂                k                                      ⁢                          ⅆ              k                                +                                                    ∂                                  ω                                      1                    ⁢                    e                                                                              ∂                n                                      ⁢                          ⅆ              n                                                          (        5        )            
When an operating frequency is fixed to a specific value, dω1e=0. When the expression is solved with respect to dk, the following relationship is obtained:
[Ex. 6].
                              ⅆ          k                =                              -                          1                                                ∂                                      ω                                          1                      ⁢                      e                                                                                        ∂                  k                                                              ⁢                                    ∂                              ω                                  1                  ⁢                  e                                                                    ∂              n                                ⁢                      ⅆ            n                                              (        6        )            An amount of variation of n when the switch-off state is changed to the on state is represented by Δn. In the case where the amount of variation is minute, the following is held:
[Ex. 7]
                                          k                                          1                ⁢                e                            ,              on                                -                      k                                          1                ⁢                e                            ,              off                                      ≅                              -                          1                                                                                          ∂                                              ω                                                  1                          ⁢                          e                                                                                                            ∂                      k                                                                                                                              k                    =                                          k                                                                        1                          ⁢                          e                                                ,                        off                                                                              ,                                      n                    =                                          n                      off                                                                                                    ⁢                                    ∂                              ω                                  1                  ⁢                  e                                                                    ∂              n                                ⁢          Δ          ⁢                                          ⁢          n                                    (        7        )            The same relationship is held for the odd mode, similarly.
Since the shift amount of the dispersion curve due to the variation of the parameter n is substantially constant, the following relationship can be established.
[Ex. 8]
                    ∂                  ω                      1            ⁢            e                                      ∂        n              ≅                  ∂                  ω                      1            ⁢            o                                      ∂        n              =  CBy using this relationship, Lsw can be expressed as follows:
[Ex. 9]
                                                                        L                sw                            ≅                            ⁢                                                                    (                                                                  2                        ⁢                        m                                            +                      1                                        )                                    ⁢                  π                                                                                            -                                              1                                                                              ∂                                                          ω                                                              1                                ⁢                                e                                                                                                                                          ∂                            k                                                                                                                ⁢                                                                  ∂                                                  ω                                                      1                            ⁢                            e                                                                                                                      ∂                        n                                                              ⁢                    Δ                    ⁢                                                                                  ⁢                    n                                    +                                                            1                                                                        ∂                                                      ω                                                          1                              ⁢                              o                                                                                                                                ∂                          k                                                                                      ⁢                                                                  ∂                                                  ω                                                      1                            ⁢                            o                                                                                                                      ∂                        n                                                              ⁢                    Δ                    ⁢                                                                                  ⁢                    n                                                                                                                          =                            ⁢                                                                    (                                                                  2                        ⁢                        m                                            +                      1                                        )                                    ⁢                  π                                                                      (                                                                  -                                                  1                                                                                    ∂                                                              ω                                                                  1                                  ⁢                                  e                                                                                                                                                    ∂                              k                                                                                                                          +                                              1                                                                              ∂                                                          ω                                                              1                                ⁢                                o                                                                                                                                          ∂                            k                                                                                                                )                                    ⁢                  C                  ⁢                                                                          ⁢                  Δ                  ⁢                                                                          ⁢                  n                                                                                        (        8        )            In order to reduce the length Lsw, a difference between the followings:
[Ex. 10]
            ∂              ω                  1          ⁢          e                            ∂      k        ⁢          ⁢  and  ⁢          ⁢            ∂              ω                  1          ⁢          o                            ∂      k      that is, a difference in group velocity between the even mode and the odd mode is increased, whereby the length can be shortened.(Definition of Bandwidth)
The propagation constant of the eigen mode of a directional coupler is varied depending on a frequency. Therefore, a phase difference between the even mode and the odd mode after the propagation of a predetermined distance fluctuates depending on the frequency of the propagation light. For a directional coupler which is designed so that light incident on the side A at a certain frequency (operating frequency) ωo can be taken out from the side B, when light of a different frequency is incident, deviation occurs in a phase difference between the even mode and the odd mode at the emitting end. Therefore, the output from the side B is decreased, and some light may be emitted from the side A. Consequently, a frequency range in which the variation in phase difference between the even and odd modes at the emitting end falls within an allowable amount φ is defined as a bandwidth.
(Conditions for Widening a Bandwidth)
An allowable phase difference is set to ±φ. Consideration is performed for the switch-off state. At the operating frequency, Expression (1) is held. When the wave numbers of the regions 1 and 2 in the case where the operating frequency is deviated by Δωoff are k′1e,off, k′1o,off, k′2e, and k′2o, respectively, the relationship with respect to the allowable phase difference is as follows:
[Ex. 11]Lsw(k′1e,off−k′1o,off)+Lfix(k′2e−k′2o)=(2m+1)π+φ  (9)When Expression (1) is subtracted from Expression (9), the following is obtained:
[Ex. 12]Lsw{(k′1e,off−k′1o,off)−(k1e,off−k1o,off)}+Lfix{(k′2e−k′2o)−(k2e−k2o)}=φ  (10)Based on the differential expression (5) of the dispersion relationship, in this case, the frequency fluctuates, and the refractive index is constant, so that the following can be represented.
[Ex. 13]
                                          k                                          1                ⁢                e                            ,              off                        ′                    -                      k                                          1                ⁢                e                            ,              off                                      ≅                              1                                                                                ∂                                          ω                                              1                        ⁢                        e                                                                                                  ∂                    k                                                                                                                k                  =                                      k                                                                  1                        ⁢                        e                                            ,                      off                                                                      ,                                  n                  =                                      n                    off                                                                                ⁢          Δ          ⁢                                          ⁢          ω                                    (        11        )            
Since the differences of other wave numbers can be represented similarly, Expression (10) can be expressed as follows:
[Ex. 14]
                                                        L              sw                        (                                                            1                                                                                                              ∂                                                      ω                                                                                          1                                ⁢                                e                                                            ,                              off                                                                                                                                ∂                          k                                                                                                                                                          k                        =                                                  k                                                                                    1                              ⁢                              e                                                        ,                            off                                                                                              ,                                              n                        =                                                  n                          off                                                                                                                    ⁢                Δ                ⁢                                                                  ⁢                                  ω                  off                                            -                                                1                                                                                                              ∂                                                      ω                                                                                          1                                ⁢                                o                                                            ,                              off                                                                                                                                ∂                          k                                                                                                                                                          k                        =                                                  k                                                                                    1                              ⁢                              o                                                        ,                            off                                                                                              ,                                              n                        =                                                  n                          off                                                                                                                    ⁢                Δ                ⁢                                                                  ⁢                                  ω                  off                                                      )                    +                                    L              fix                        (                                                            1                                                                                                              ∂                                                      ω                                                          2                              ⁢                              e                                                                                                                                ∂                          k                                                                                                                                  k                      =                                              k                                                  2                          ⁢                          e                                                                                                                    ⁢                Δ                ⁢                                                                  ⁢                                  ω                  off                                            -                                                1                                                                                                              ∂                                                      ω                                                          2                              ⁢                              e                                                                                                                                ∂                          k                                                                                                                                  k                      =                                              k                                                  2                          ⁢                          o                                                                                                                    ⁢                Δ                ⁢                                                                  ⁢                                  ω                  off                                                      )                          =        ϕ                            (        12        )            
                              Δ          ⁢                                          ⁢                      ω            off                          =                  ϕ                                                                                                                L                      sw                                        ⁡                                          (                                                                        1                                                                                                                                                      ∂                                                                      ω                                                                                                                  1                                        ⁢                                        e                                                                            ,                                      off                                                                                                                                                                        ∂                                  k                                                                                                                                                                                                                  k                                =                                                                  k                                                                                                            1                                      ⁢                                      e                                                                        ,                                    off                                                                                                                              ,                                                              n                                =                                                                  n                                  off                                                                                                                                                                    -                                                  1                                                                                                                                                      ∂                                                                      ω                                                                                                                  1                                        ⁢                                        o                                                                            ,                                      off                                                                                                                                                                        ∂                                  k                                                                                                                                                                                                                  k                                =                                                                  k                                                                                                            1                                      ⁢                                      o                                                                        ,                                    off                                                                                                                              ,                                                              n                                =                                                                  n                                  off                                                                                                                                                                                        )                                                        +                                                                                                                          L                    fix                                    ⁡                                      (                                                                  1                                                                                                                                            ⅆ                                                                  ω                                                                      2                                    ⁢                                    e                                                                                                                                                              ⅆ                                k                                                                                                                                                                      k                            =                                                          k                                                              2                                ⁢                                e                                                                                                                                                        -                                              1                                                                                                                                            ⅆ                                                                  ω                                                                      2                                    ⁢                                    o                                                                                                                                                              ⅆ                                k                                                                                                                                                                      k                            =                                                          k                                                              2                                ⁢                                o                                                                                                                                                                          )                                                                                                          (        13        )            The obtained result Δωoff is the bandwidth in the switch-off state. The bandwidth in the switch-on state can be obtained in the same way. The bandwidth of a directional coupler switch falls within a common range of the bandwidths in the switch on and off states. In order to increase the bandwidth, the denominator of Expression (13) should be reduced. In other words, a difference between the followings:
[Ex. 15]
            ∂              ω                  1          ⁢          e                            ∂      k        ⁢          ⁢  and  ⁢          ⁢            ∂              ω                  1          ⁢          o                            ∂      k      that is, a difference in group velocity should be reduced.(Trade-Off Relationship)
As described above, in order to shorten the switching length, it is necessary to increase the difference in group velocity between the even mode and the odd mode. However, in order to widen the bandwidth, it is necessary to decrease the difference in group velocity. They contradict each other.
In this way, they are in a trade-off relationship. For this reason, in a conventional directional coupler switch which is configured by a simple symmetric parallel waveguide, either of the switching length or the bandwidth may be sacrificed.